To factor the expression \( 12x^2 - 27 \), we can follow these steps:

1. **Identify the Greatest Common Factor (GCF)**:
   The GCF of 12 and 27 is 3.

2. **Factor out the GCF**:
   \[
   12x^2 - 27 = 3(4x^2 - 9)
   \]

3. **Recognize the difference of squares**:
   The expression \( 4x^2 - 9 \) is a difference of squares, which can be factored as follows:
   \[
   4x^2 - 9 = (2x - 3)(2x + 3)
   \]

4. **Combine everything**:
   So, the fully factored form of \( 12x^2 - 27 \) is:
   \[
   3(2x - 3)(2x + 3)
   \]

### Final Answer:
\[
12x^2 - 27 = 3(2x - 3)(2x + 3)
\]

Do you want details on any specific steps or have any questions? Here are some related questions you might consider:

1. What is the significance of the difference of squares in factoring?
2. Can you factor other polynomial expressions using the same method?
3. How would you solve the equation \( 12x^2 - 27 = 0 \)?
4. What other methods can be used to factor polynomials?
5. How do you verify that your factorization is correct?

**Tip:** Always check for a GCF first before attempting to factor further.

Discover how to factor the expression 12x^2 - 27 using the GCF and the difference of squares. This step-by-step guide includes the identification of the GCF and provides a full solution suitable for students in Grades 8-10.

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